Probability Density Estimation Using Isocontours and Isosurfaces: Applications to Information-Theoretic Image Registration

Abstract

We present a new geometric approach for determining the probability density of the intensity values in an image. We drop the notion of an image as a set of discrete pixels and assume a piecewise-continuous representation. The probability density can then be regarded as being proportional to the area between two nearby isocontours of the image surface. Our paper extends this idea to joint densities of image pairs. We demonstrate the application of our method to affine registration between two or more images using information-theoretic measures such as mutual information. We show cases where our method outperforms existing methods such as simple histograms, histograms with partial volume interpolation, Parzen windows, etc., under fine intensity quantization for affine image registration under significant image noise. Furthermore, we demonstrate results on simultaneous registration of multiple images, as well as for pairs of volume data sets, and show some theoretical properties of our density estimator. Our approach requires the selection of only an image interpolant. The method neither requires any kind of kernel functions (as in Parzen windows), which are unrelated to the structure of the image in itself, nor does it rely on any form of sampling for density estimation.

Graph Similarity through Entropic Manifold Alignment

“…Let β be the inverse temperature corresponding to a given iteration, and let us approximate the current adjacency matrix as suggested above: A = 1 r (11 T − I), where r = exp(β). Let E be the so-called N × N perturbation matrix defined by (40) E ab = h if a = i and b = j, 0 otherwise, where h > 0. Then = A+E is the linearly perturbed adjacency matrix.…”

“…The correspondence function establishes a common reference system as in the case of image alignment [36], [40]. However, the optimal transformation T is not needed here since it is not going to be applied to f Y (u) with u ∈ V Y .…”

Relation-Aware Isosurface Extraction in Multifield Data

“…Rajwade et al [22] use the JPD for two scalar fields in the context of computing mutual information and solving the image registration problem. The scalar fields are essentially grayscales of the two images that are to be registered.…”

An information theory perspective on computational vision

“…The intensities of corresponding points in the images may differ greatly but mutual information is largely invariant to these transformations and so can yield good matching. Recent work has lead to greater understanding of why this measure is so effective [74].…”